Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2023
• Hauptverfasser: Ebrahimi-Fard, Kurusch, Patras, Frédéric, Tapia, Nikolas, Zambotti, Lorenzo
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2023
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211905
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability. Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia and Lorenzo Zambotti. SIGMA 19 (2023), 038, 17 pages

We study a particular group law on formal power series in non-commuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra. This group law is left-linear and is therefore associated with a pre-Lie structure on formal power series. We study thes...